Absolute Counting in the endgame by O Meien and translated by John Fairbairn
has just been published.

For details on the book you may visit the publisher's website:
http://www.boardnstones.com/09-All_Titles-021-BNS021.php

Here, I would like to take the opportunity to quote John Fairbairn from the Translator's Note in the book:

"The origin of this translation goes back some years to when an endgame discussion took place on the Life in 19×19 internet forum. As a lifelong numerophobe, I was somewhat out of place there, but I had looked at O Meien’s book previously, and I could see that what Western experts said sometimes differed markedly from what O Meien said. Not understanding the topic well enough myself, but still wanting to contribute, I decided that the best way was to quote O Meien instead.
I therefore translated small tracts and posted those. Over time more tracts were added, and I found it easier in the end – to maintain consistency and so on in a topic that required precision – just to translate the whole text for myself. I stopped posting when the 10% “fair use” limit was looming, and then the whole text got filed away and forgotten, until Gunnar Dickfeld got wind of it.
He secured the necessary permissions, and by chance also discovered this his edition of 2013 now contained a little more than
my 2004 edition. Evidently, O Meien had been convinced of the need to explain a couple of things even more clearly for even a Japanese audience. Those bits have now been incorporated."

For these discussions on L19 see:

Amazing discovery confirms the end is not nigh

Can a double sente position exist?

Thank you, John, for your efforts in translating this book as a whole and making it available to a wider audience.

How to order
The book can be ordered online from well-known and lesser-known shops by searching for the ISBN (ISBN 978-3-98794-021-7) or the title.

_________________
www.boardnstones.com

My copy arrived last week. I recommend this book. There's lots of good ideas for players from around 5 kyu through to mid dan level (possibly higher; I'm not qualified to say). You can see some excerpts from the book, and lots of discussion, in John's previous threads at Boundary plays - O Meien's method and Boundary plays - O Meien's method (Part 2)

The book reminds me a little bit of Rational Endgame: each section is clear and easy to follow, but it jumps around a bit, and feels like it should include a few more topics to help us join the dots. In some ways it goes further than Rational Endgame: there are some good examples of choosing the right sequence to play out multiple positions, and applications to real games. Overall it's a longer book, 180 pages of main text plus front matter, and good value for money, but I still wanted more :-)

If you've been hanging around these forums for a while, you'll have seen the discussions of deiri counting and miai counting in the endgame. This book explains both from the very beginning. Deiri is the traditional system, and miai is a more modern approach. The old Ogawa/Davies book from the Elementary Go Series and Get Strong at the Endgame both use deiri counting; Rational Endgame and Robert Jasiek's books use miai counting. As far as I can tell, "absolute counting" is O Meien's name for miai counting plus some philosophy on how to apply this method.

It's a book of two halves, where chapters 1-3 explain how to count, and then chapters 4 and 5 apply this to real games, with three positions from amateur games in chapter 4 and eight complete pro games (six of them featuring the author) given in chapter 5. My impression is that the second half is much more advanced than the first: this is where I'd like to see some extra chapters in the middle to bridge the gap. Some examples on 9x9 and 13x13 boards would help, as well as examples of how to find the right move in "vague" positions in the centre of the board. Parts of chapter 5 are a little over my head. I like that in a book: it means I can keep coming back to it and learning more over the years, but there's also enough "easy" (or not too hard) parts that I won't give up.

The introduction shows two positions where the old method of deiri counting might give you the wrong impression. These aren't explained in detail just yet: this chapter is just a teaser, and the explanations follow in chapter 2 after you've learned a bit of theory.

Chapter 1 is called "How to count territory". There are 26 problems, starting with single-move gote sequences with a whole number of points, and progressing to half points and followup moves. The prose style is very conversational, a bit reminiscent of Kageyama. The explanations talk you through not just the mechanics of calculating the answer, but also the thought process, some questions or misconceptions that might occur to you, some mental shortcuts, words of encouragement, and so on. Sometimes this is nice; at other times I got a little irritated, feeling that I didn't really need four paragraphs of chatty prose to remind me that four divided by two makes two.

I think all of the problems are meant to be "elementary", and indeed I think the first half of the chapter would make sense to a 10 kyu player. But he seems to forget that what's obvious to a 9 dan pro is not always obvious to an amateur. Before you can count the position, you need to see the best first move for each player and read out the followup moves accurately. Some of the later problems in the chapter had me pausing for a few minutes to check my reading.

Chapter 2 is called "The value of one move". This is more theoretical, but with clear and well chosen examples. It gets more into the nuances of sente and gote, the concept of "privilege", and the difference between deiri and miai counting. There are some examples where "count each region and play the biggest move" actually gives an incorrect result, and he gives some good principles on how to handle these situations.

Chapter 3 is about endgame kos. He's keen to convince the reader that it's not really as hard as it looks. This chapter explains the fine details of how to count "a third of a point" (and a quarter for a two-stage ko) and has some good big-picture discussions of evaluating trades. There's a curious example part way through where he looks at a key decision point in game 7 of the 28th Kisei final. It's interesting but needs a lot more explanation. I had to run up KataGo to explain to me why the choice of move in the corner means you can't block in the middle: another place where perhaps the author forgets that deep reading doesn't come naturally to we amateurs. Apart from that moment though, all the explanations are as clear and useful as the rest of the book.

In all of chapters 1-3, O gives intuitive reasons for trusting the theory, but doesn't get into rigorous explanations of exactly why it works. Some people will see this as a strength: the book is accessible and easy to follow, and even if it's sometimes imprecise, it's better than not knowing any theory at all. Some people may be disappointed, and be looking for something more like the combinatorial game theory literature or Robert Jasiek's books. Overall though, I think Absolute Counting is a big step up from the older literature.

Moving on to what I think of as the second half of the book: chapter 4 gets into real game examples on a 19x19 board. He gives three positions from near the end of an amateur game and asks if you can evaluate the position (that is, who is ahead and by how many points). This is where you can take what you've learned in the first half an put it into practice -- but it's a sudden and large step up in difficulty.

Each example gets 4-7 pages of explanation. It's really helpful to see his thought process: first looking at each part of the board separately, reading out some sequences, then putting them in order, looking ahead to a nearly completed position that's easier to count, getting a preliminary count, looking a bit further ahead, checking the count, ...

The chapter title is the curious phrase When to play "Certainties". One of the recurring themes here is that you shouldn't expect to read to the very end of the game and calculate the final score. (He doesn't say it that way; this is my interpretation.) You're always going to be in some doubt as to exactly where you stand. But you can estimate a "margin of error". So you should be able to tell the difference between "I'm probably a little bit ahead but it could go either way" (large margin of error) versus "I'm about 5 points ahead with a 3 point margin of error so I've definitely won". (The combinatorial game theorists will recognise this as a veiled reference to the temperature of the position.)

I found the choice of examples a little bit strange. My hope is that by learning to count more accurately, I can make better decisions at the board. But in fact, we see examples where there's an obvious biggest move or clear-cut forcing moves, so you're going to play the same way regardless of the count; and one example of a decision point where the answer turns out to be "you win either way". Despite this, the method of analysis is valuable, and I think going through this chapter a few times will improve my play.

Chapter 5, "Analysis of Endgames in Actual Games", seems to be more of the same, but on a higher level. To be honest, I haven't finished this chapter: each example deserves several hours of study, and I wanted to publish this review before the end of the year! My first impression is that the choice of examples is better than chapter 4: there are cases where the count actually does influence the choice of move. Because it's mostly the author's games, we get the inside view of where he felt confident, where he was uncertain, and how he prioritised his efforts if he couldn't read out 100% of the details. It's the longest chapter of the book, 66 pages for 9 examples, averaging more than 7 pages of discussion for each endgame. Some of the discussions have summary paragraphs at the end, or a block of prose half way through, drawing out some principles so that you don't just drown in the details. I'm going to enjoy working through all of this.

The layout is clear and spacious, with a slightly larger font than usual, easy on the eyes without wasting space. I found the non-square diagrams slightly disconcerting; it's not so obvious for the smaller diagrams, but the large full-board diagrams at the start of each example in chapters 4 and 5 are obviously taller than they are wide (yes, I'm obsessive enough to get the ruler out and check, and also compare some other books: they're square on every other book I looked at). I guess I'll get used to it, and it might not bother some people. There are also some small typos, but nothing harmful; I haven't noticed any errors in the calculations.

The translation by John Fairbairn is excellent as usual. The last part of the translator's introduction, talking up the alleged complexity of miai counting and making some rather strange analogies with corporate accounting, strikes me as unhelpful. Don't be put off: it's not as bad as he makes out! But John has done us a great favour in translating this book, so we can forgive him a moment on his own soapbox :-) I hope there will be a sequel.

Hi all, I have bought this book (I love the writing style) and am working through it. It really answers a lot of my questions! There is one concept, though, which makes me stumble: the subsection "the relationship between reverse sente and gote boundary play" starting on page 72.

O Meien says on page 76: "In cases where a reverse sente and a gote play of apparently similar size are bound up together, the procedure is: (1) ... (2) ... ." I don't understand how plays can be bound up together. To me, all boundary plays in the examples are independent, like, they can be played out in any order, wherever they would be on the board.

To give an example: let's say we have three boundary plays left, in reverse sente (RS) and gote (G): 5 RS, 12 G, and 10 G.

If black thinks 5 RS and 12 G are bound up together, they should (1) calculate the deficit of the number of points of playing the RS move without regarding sente/gote (5-12=7) and then (2) check whether they can recover it with the next gote move, which is 10 points, so the answer is yes.

Black gets 5 RS, white gets 12 G, black gets 10 G, so 15:12. If Black plays 12 G, white gets 5 sente + 10 G, ao 12:15. So the rule seems to work.

Now lets look at FOUR moves left: 5 RS, 12 G, 10 G, 6 G. Still black thinks 5 RS and 12 G are bound up together, sees 10 G on the board and decides to play 5 RS, white 12 G, black 10 G, white 6 G, so 15:18. However, if black had played the gote move now, 12 G for black, 5 sente + 10 G for white, 6 G for black, so 18:15, which is better.

Now we actually have problem G on page 78 (5 RS, 12 G, 10 G) with a 6 G somewhere else on the board. Unfortunately, if I change this again to 5 RS, 12 G, 10 G, 6 G, 4 G, the correct decision changes again.

So does the rule actually only apply if we assume the last reverse sente plays as well as ALL gote plays bar the smallest one are bound together?

What I see would work is a much more complicated rule like: sort all remaining gote moves in descending order. If black plays RS, then white will get gote moves ranked 1, 3, 5, ... and black RS, 2, 4, 6, ... , as many as there are. If black plays a gote move first, white will get RS, 2, 4, 6 ... and black 1, 3, 5, ..., which is the precise opposite. So the decision rule would be to add all odd entries on that list, and RS plus all even entries on that list, and decide what you want for yourself.

Can someone please help me unmuddle my muddled mind? ^-^

The general order of, even if simple, local endgames of different types (and larger than requiring anaylsis by infinitesemals) on the board is difficult.

The first classification should be between

1) early endgame (cannot be solved by Reading and Counting) versus

2) late endgame (could be solved by Reading and Counting but other methods might be faster)

because different theories apply.

For the late endgame, the following classes of positions have been solved:

3) one simple local endgame (local gote, ambiguous or local sente; in the latter, a player has a sente play while instead the opponent has a reverse sente play) with follow-up in an environment of simple gotes without follow-ups (solved by Bill Spight or me)

4) one simple local gote endgame with follow-ups of both players in an environment of simple gotes without follow-ups (solved by me)

For the late endgame, the following classes of positions have been partially simplified:

5) the position has at least two local endgames with simple follow-ups of the same player (simplifications by Bill Spight and me)

6) the position has at least two local endgames with iterative follow-ups (simplification by me)

For the early endgame, we can first distinguish positions

7) with an ensemble so that there is a significant drop in move values between the ensemble and
environment (Bill Spight and I suggest first to solve only the ensemble by assuming, e.g., an ideal environment)

8) without an ensemble

For the early endgame without an ensemble, the following classes of positions have been solved as a good approximation (making assumptions such as iterative local endgames essentially behaving like simple local endgames, no wild fights, no kos and no infinitesemals needed for the last move of the game):

9) one simple local gote endgame with follow-up in an idealised environment (solved by me)

10) one simple local sente endgame with follow-up in an idealised environment (solved by me)

11) one local endgame with gote and sente options (solved by Bill Spight or me)

For the early endgame, the following class of position has been partially simplified:

12) the position has at least two local endgames with simple follow-ups of the same player (simplifications by Bill Spight and me)

***

Now, when O Meien speaks of a reverse sente play and a gote play, he means what I call a position with a local sente endgame and elsewhere a local gote endgame and the preventer having the turn. In a local endgame with one player's follow-up, the preventer is the opponent who, by playing there first, prevents the player from making the follow-up available. Some theory of Bill Spight and me applies to a local endgame with one player's follow-up regardless of whether the local endgame is a local gote, ambiguous or a local sente. Therefore, in general, one must not speak of the reverse sente player. The preventer happens to be the reverse sente player if the local endgame with one player's follow-up happens to be a local sente. That is, theory for a local sente is less general than theory for a local endgame with one player's follow-up.

You paraphrase O Meien with "the procedure is: (1) ... (2) ...". Since I only have the Japanese original and cannot read the text, please tell us the details of the suggested procedure! Also please clarify whether we are in the early or late endgame.

Plays at different parts of the board can be "bound up together" by theory if the position allows its application. This can be so for Bill Spight's or my theory because we have stated mathematical theorems and proved them. Whether it also is so for O Meien's suggestions we might discuss when you cite them.

For your examples with reverse sente plays and gote plays, you need to provide more information: Is the reverse sente in a simple local sente endgame? Is it the preventer's turn? Is each gote play in a simple local gote without follow-up or what else? Do we have information on the environment, such as the temperature and the second-largest move value?

After your answer, further diving into subclasses of positions might become necessary for low or high temperature etc. I think that O Meien has not entered such of what Bill Spight or I have studied and partially solved. However, it might be that for some kinds of positions O Meien's suggested theory is sufficient or there are relations to our theory, in which case we might provide deeper explanations.

The full quote is just a longer version of what I wrote further down in my post:

... the procedure is:
[1] Calculate the deficit as a number of points disregarding sente and gote in the case where you play the reverse sente;
[2] If it appears that you would recover that deficit with the next boundary play, play the reverse sente. If you would not recover it, make the gote play instead and so maintain your advantage.

I don't yet know about early/late, etc., but thanks for the valuable comments. I'll reply to your detailed questions after having worked through the whole book, hoping I'll have an answer by then.

Does you mathematical theory base in any way on the work of Elwyn Berlekamp, who gave half of the name to the Berlekamp-Massey algorithm? I'm mostly asking because I knew Massey, not becuse I really understood Berlekamp's endgame theory.

"deficit" and "recover" in your procedure citation are not self-explaining so I am unsure what is meant, although I know the basics of O's method. My guess of how to apply it would ignore the procedural text.

My mathematical theory is a fresh approach to endgame maths and conceptually relies mostly on just school maths. Only occasionally, I needed to use combinatorial game theory a la Siegel. I (and Bill Spight) do not rely on Berlekamp's / Wolf's maths but we prefer to avoid it. I even go so far to replace some of Berlekamps infinitesemals by school maths (such as using parity) to ease application.

My typical endgame maths compares two terms to see which is the larger one and represents the move to choose.

Infinitesemals are useful for the last move of the game but nothing but a burden earlier during the game. Therefore, I avoid them and study the preferably larger endgames.

You're doing fine. You've found the most imprecise part! O Meien's suggested procedure is not a rule. It's a heuristic that will produce fewer errors than just playing the largest move value every time, but it's not entirely accurate.


Correct. "Bound up together" is either the author or translator being a little casual with language. More likely the author I suspect. It's convenient to have both local positions on the same diagram, but the analysis would be the same if they were on opposite sides of the board.


Well, the original point of this thread was to encourage people to buy the book :-) I'm keen to see more books of this nature published, so I was happy to send some money to encourage the publisher and the translator. Consider whether you're willing and able to do the same.

I'll paraphrase some more. In chapter 3, there are three examples with the following features:

• A diagram with two local positions: from black's perspective, a reverse sente A and a simple gote B.
• There are no local followup moves.
• The deiri values are a and b respectively, with 2a > b > a, so that the miai values are a and b/2 with A being the larger move.

We're asked to compare two options:

• Option 1: black plays A, white plays B, and black gets the first play elsewhere on the board
• Option 2: black plays B, white plays A, black answers, and white gets the first play elsewhere.

With option 1, black has essentially paid b-a points in exchange for sente. In general, this is a good idea, but it's clearly a mistake if A and B are the only two remaining plays on the board. It seems that the author is trying to lead the reader to discover the concept of tedomari without actually using the technical term.

"The procedure" is: (1) calculate the value of b-a, and then (2) if the largest move elsewhere is worth at least b-a points, then play A, otherwise play B.

When we are looking at endgame moves as numbers which the players alternatively lay claim to then the gote moves are impartial (or if you wish to put it differently, equitable or symmetric) but the reverse sente moves are not. Being impartial means that the gote moves can be played by either player and there is no other difference than which player lays claim to the points by making the move. The reverse sente on the other hand already belongs to the opponent (the player that can play it in sente), that player is usually said to have the right (or privilege) to play those moves. This is hugely important, and easily forgotten when listing moves as numbers and trying to reason about what order to pick those numbers in.

With this case, let a = 5 RS, b = 12 G, c = 10 G, d = 6 G, we have three gote moves (b, c, d) that have to be played in a fixed order and one reverse sente move (a) which can be used to change which player is first to the spoils.

Now it is a that should be compared with the difference between playing first or second in the b, c, d sequence of gote moves. You can set up a formula for this in different ways, for example ask if b - a >= c - d and each such formula could be put into different words. The whole thing can also be made clearer and simpler if we only work with cases where d = 0 but in general you could have a long list of gote moves and more than one reverse sente.

This example was already a bit unwieldy and imagine if you were playing a game and trying to make heads and tails of something with N gote moves and M reverse sente moves. It is more practical to just notice that in a few moves the gote moves will be smaller and the chance to play a reverse sente is arising. Maybe the approach of this book is to teach something in a similar vein that can build intuition instead of getting the readers bogged down with something they will find impossible to apply in their own games. That seems like the right approach to me, more advanced applications can anyway come naturally to players that have good intuition for the endgame.

All books about modern endgame theory should be read because the endgame is important, there are only a few such books and they are all at least good because the contents of every such book is correct or essentially correct. It is just that I have already "read" the original, a few weeks ago looked into the translated book, considered whether it would provide me sufficient new insight beyond the original and decided "insufficient for getting a second copy". Everybody not having read the original should read the English version though, regardless of whether having read all other books on the topic. More information on the topic is good for one's endgame understanding as long as there are still only a few books on the modern endgame topic at all in the literature.



Ah, this explains hanspi's example values! :)



It seems that this is meant for the early endgame with A and B being an ensemble before a significant drop in move values.

For this, in Endgame 4 - Global Move Order, chapter 4.1, I write:

"We solve the ensemble by assuming an ideal environment. [...] T/2 is a good approximation of the net profit of starting, then alternating, in the ideal environment. (*) [...] After play in the ensemble, we predict the score by making a territorial positional judgement in the settled regions and assuming the value T/2 for the environment in favour of its starting player."

Here, T is the temperature, of course, which is the modern move value of the largest move elsewhere.

Now, it is an exercise to understand why these ensemble parts of the theory of O Meien and me agree to each other.

(*) had been suggested by Bill Spight, who must have proved it for himself but implicitly motivated me to find the easy proof again and publish it first on L19x19.

I'm not by any stretch a mathematical endgame expert, but what I think you have stumbled upon is the concept of tedomari--the last play. If there are an odd number of plays and one is reverse sente then you can take the reverse sente and you and your opponent will split the remaining moves, presumably in some kind of decreasing order. Naively I expect the math to be fairly straightforward here.

There seems to be an endgame concept that the last play, or the last play within a similarly sized group of plays, is worth more than usual because the following plays are worth much less.

Sensei's Library has an entry that may be helpful.

While getting tedomari is often correct, I have shown by counter-example that letting the opponent get tedomari is sometimes correct.

In the general case, I expect the parity to be immaterial. Suppose an example with an odd number of plays and a sufficiently large board. Modify the example by multiplying each move value by 10. Add another simple local gote with the move value 1/2. Now there is an even number of plays but the behaviour should still be essentially the same.

In an ideal environment with constant drops, such as 1, parity can have an impact more easily.

I am living in Korea, cannot order here, any chances to get it on gobooks?